1973 AMC 12 Problem 33

Question

When one ounce of water is added to a mixture of acid and water, the new mixture is

20\%

acid. When one ounce of acid is added to the new mixture, the result is

33\frac13\%

acid. The percentage of acid in the original mixture is

22\%

24\%

25\%

30\%

33\frac13\%

Let

x

and

y

be the original ounces of water and acid

Write one concentration equation after adding water and another after subsequently adding acid

Let the original mixture contain

x

ounces of water and

y

ounces of acid. The two additions give

\begin{aligned} \frac{y}{x+y+1}&=\frac15,\\ \frac{y+1}{x+y+2}&=\frac13. \end{aligned}

These simplify to

x+1=4y, \qquad x=2y+1.

Hence

y=1

and

x=3.

The original acid percentage was

100\cdot\frac{y}{x+y} =100\cdot\frac14=25\%.

Therefore, the correct answer is C.

Problem 33 in other years